Air is blowing with a wind speed of 35 [mi/hr] eastward relative to the ground.Find the velocity of an eagle relative to an observer on the ground if the eagle is flying at a speed of 22 [mi/hr] westward “against” the wind.
To find the velocity of the eagle relative to an observer on the ground, we can use vector addition.
First, let's assign a positive velocity to the eastward direction (since the wind is blowing eastward) and a negative velocity to the westward direction (since the eagle is flying westward against the wind).
The wind velocity is given as 35 [mi/hr] eastward. Since the eagle is flying against the wind, we can consider its velocity as -22 [mi/hr] westward.
To find the velocity of the eagle relative to the observer on the ground, we add the wind velocity and the eagle's velocity:
Velocity of the eagle relative to the observer = Wind velocity + Eagle's velocity
Velocity in the eastward direction is positive, so the wind velocity contributes +35 [mi/hr], while the eagle's velocity is westward (-22 [mi/hr]).
Adding these two vectors gives us:
Velocity of the eagle relative to the observer = 35 [mi/hr] + (-22 [mi/hr])
When adding these velocities, we take the magnitude of the wind velocity and subtract the magnitude of the eagle's velocity, while keeping the direction (in this case, east or west).
So,
Velocity of the eagle relative to the observer = 35 [mi/hr] - 22 [mi/hr]
Simplifying, we get:
Velocity of the eagle relative to the observer = 13 [mi/hr] eastward
Therefore, the velocity of the eagle relative to an observer on the ground is 13 [mi/hr] eastward.